On the reverse jacket matrix for weighted Hadamard transform

The class of reverse jacket matrices [RJM(H)] and the corresponding restclass RJM(H) [RRJM(H)] are defined; the main property of RJM(H) is that the inverse matrices of its elements can be obtained very easily and have a special structure. RJM(H) is derived using the weighted Hadamard transform corresponding to the matrix X and a basic symmetric matrix Λ. Each element of RJM(H) is a generalized Quincunx subsampling matrix. In this brief we represent, in particular, the systematical blockwise extending method for RJM(H). We have deduced a new orthogonal matrix M₁∈RRJM(H) from a nonorthogonal matrix M₀∈RJM(H). These matrices can be further used to develop efficient algorithms in PCS signal processing as well as in coding and information theory. Using several classes to extend RJM(H) and RRJM(H), we illustrate some examples for multilevel structures